Name Period Final Exam Review

Transcription

1 Name Period Final Exam Review

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3 1. Given XXXXXX where X(0,6), Y(4, -2), and Z(-4, -2), use the grid to below to dilate the figure by a scale factor of 1. What are the new coordinates? 2 2. What is the slope of the line pictured in the graph below?

4 3. When finding the slope of a line on a graph find the and divide by the. When finding the slope of a line given two points use. When finding the slope of a line given an equation in slope-intercept form, the slope is next to the. Calculate the slope of the line. 4. What is the equation of the following graph?

5 5. Graph the equation yy = 3xx 2. Make a table if needed. 6. Solve the inequality and graph the solution. a + 3 > 8 7. Solve the inequality and graph the solution.

6 8. A rectangle is dilated by a scale factor of 1 to create a new rectangle. 2 a. Choose dimensions for the rectangle. Length: Width: b. Find the perimeter of the rectangle. P = c. Find the area of the rectangle. A= d. Dilate the rectangle s side lengths by ½ to get the new dimensions. Length: Width: e. Find the new perimeter of the rectangle. P = f. Find the new area of the rectangle. A= g. Compare the original perimeter and area with the new perimeter and area. The new perimeter is the perimeter of the original perimeter. The new area is the area of the original area. 9. If a square has a perimeter of 12, and then is multiplied by a scale factor of 4.5, what will the new perimeter be?

7 10. Draw a right triangle with the side lengths of a=6, b=8, and c=10. a. What is the perimeter of the triangle? P = b. What is the area of the triangle? A= c. Dilate the figure by a tripling the side lengths and record the new lengths. a = b = c = d. What is the perimeter of the new triangle? P = e. What is the area of the new triangle? A= f. Compare the original perimeter and area with the new perimeter and area. The new perimeter is the perimeter of the original perimeter. The new area is the area of the original area. 11. Use the following image to answer the questions below. a. Calculate the perimeter and area. P = A= b. Using a scale factor of 3, calculate the new perimeter and area. 4 P= A= c. How much larger or smaller is the new perimeter than the original? d. How much larger or smaller is the new area that the original?

8 12. Solve each of the following equations. x - 4 = x -6 2x = 8 + x 4x + 8 x + 2 6x = In complete sentences, explain the differences between a proportional graph and a non-proportional graph. 14. Determine if the following graphs are proportional or non-proportional. 15. Solve the following inequality. 2x x 6

9 16. The Stars Basketball League charges $40 entry fee and $10 per game. The Rockets Basketball League charges $100 entry fee and $5 per game. After how many games will the cost of The Stars Basketball League be the same or more than The Rockets Basketball League? Write an inequality and solve. 17. A photo studio offers two types of portrait plans. The first plan charges $18 per sheet and $32 enrollment fee. The second plan charges $12 per sheet and a $50 enrollment fee. For what number of portrait sheets is second plan less expensive? Write an inequality and solve. 18. In each of the following tables, determine whether the relationship between the two quantities described in the table is linear. If so, determine the constant rate of change. If not, explain your reasoning.

10 19. The equation yy = 1 xx + 1 is graphed below. List at least five points that will lie on 3 the line. 20. Determine the slope of the line that passes through the points (9, 7) and (1, 3). 21. Susan and Dale were solving for the slope of the line that passes through the points (5, 3) and (10, 13). Look over their work and determine who solved it correctly and explain why the other student didn t Susan 13 3 = 5 10 = 1 2 Dale = 10 5 = 2

11 22. Use the model below to write and solve the equation. 23. The model below represents the equation xx + 5 = 3xx 1. What value for x makes the equation true? (solve for x)

12 24. In complete sentences, explain the similarities between slope and rate of change. 25. The table below shows the change in temperature over time. Find the rate of change in degrees Fahrenheit with respect to time. 26. The table shows the number of students in four clubs at Eastwood Junior High. If the total number of students in the Ski Club and Book Club are equal to the number of members in the Math Club and Student Council, how many students are in the Book Club? Club Number of Members Ski 5(c 6) Book c Math c + 11 Student Council 24

13 27. The table shows the numbers of students in each eighth grade homeroom at Lincoln High. If the total number of students in Homerooms A and B are equal to the total number of students in Homerooms C and D, how many students are in Homeroom A? Homeroom Number of Students A a B 4(a 3) C 15 D 2a The amount of cable that is wound on a spool varies directly with the amount of time that passes. Determine the speed at which the cable moves.

14 29. Each eighth grade math teacher currently has about 23 students and gets 2 students every grading period. The equation below can be used to find s, the total number of students after g number of grading periods. ss = 2gg + 23 a. Which number represents the slope? b. Which number represents the y-intercept? 30. In complete sentences, explain what the slope represents in the previous equation? 31. In complete sentences, explain what the y-intercept represent in the previous equation? 32. What is the result of the transformation below? (x, y) (-x, y) A. Reflection across the x-axis B. Reflections across the y-axis C. 90 rotation clockwise D. 90 rotation counterclockwise

15 33. The graph of the line y = 2x + 3 is drawn on the coordinate grid below. Which table of ordered pairs contains only points on this line? A B x y x y C D x y x y

16 34. Which is the best representation of the following equation y = 2x F Graph 1 G Graph 2 H Graph 3 J Graph Which transformation does NOT produce congruent figures? A. 270 rotation about the origin B. Translation up 5 units C. Dilation by a scale factor of 3 D. Reflection over the x-axis

17 36. The vertices of a triangle are (-1, 5), (-4, 1) and (-3, 6). Which grid represents the result of reflecting the triangle across the x-axis? A. C. 37. Sam went to an amusement park. From the main entrance he used the algebraic representation (x, y) (x 10, y + 14) to walk to a ride. Which ride did Sam walk to?

18 38. If rectangle ABCD was reflected across the x-axis, what would be the coordinates of C? A. (-2, 1) B. (2, 1) C. (2, -1) D. (-1, 2) 39. Which type of transformation is illustrated in the diagram below? A. Dilation B. Reflection C. Translation D. Rotation

19 40. Figure TUVW is shown on the grid below. Which of the following shows the figure TUVW after a translation of (x, y) (x + 2, y + 3) to form the image T U V W? A. C. B. D.

20 41. What is the total surface area of the rectangular prism? 4 in. 7 in. 3 in. a. 14 in. 2 b. 25 in. 2 c. 84 in. 2 d. 122 in At Baskin Robbins an ice cream cone has a radius of 5 centimeters and a height of 8 centimeters. How many cubic centimeters of ice cream can the just the cone hold? f cm 3 g cm 3 h cm 3 j cm What is the volume of the following sphere? Write your answer in terms of pi. 9 in. a π in. 3 b π in. 3 c π in. 3 d. 972π in. 3

21 44. Mikayla is wrapping gifts for her little brother s birthday. She put all the gifts in boxes to make them easier to wrap. If one box is 12 in. by 10 in. by 2 in., what is the least amount of wrapping paper she will need for that particular box? Determine which geometric concept you would use to solve the problem. Then solve the problem. 45. Matthew is building a toy box that is 6 ft by 4 ft by 3 ft. What is the surface area of the toy box in square feet? 46. Jose s parents are tired of maintaining the swimming pool that no one uses anymore. It was a nice circular pool with a diameter of about 12 yards. Jose s parents want to fill the pool with cement so they can build a patio where the pool is. If the pool is 4 ft deep, how much cement will they need to fill the entire pool? Which geometric concept would you use to solve the problem? Solve.

22 47. A cylinder is 6 inches tall and has a diameter of 20 inches. The drawings below show the shape of the cylinder and its net. 6 in 20 6 in What is the approximate lateral surface area of the cylinder? Use the following table to complete questions Calculate the mean absolute deviation for comedies. 49. Calculate the mean absolute deviation for dramas. 50. Lauren is comparing two data sets. Data set A has a mean absolute deviation of 4.5 and data set B has a mean absolute deviation of 9.9. What conclusion can Lauren make about the two data sets? A. The average of set A is greater than the average of set B. B. The average of set A is less than the average of set B. C. The data in set A is more spread out than the data in set B. D. The data in set A is less spread out than the data in set B.

23 51. Emma deposited $825 in an account that earns 2.5% simple interest. How much interest will she earn in 3 years? 52. Josiah borrowed $12,500 to buy his new car. He is being charged 6% simple interest for 48 months. How much will Josiah pay for the car? 53. Tyler borrowed $350 from quick loan. Quick loan charges 5% interest compounded annually. How much will Tyler pay for his loan if it takes him 3 years to pay it off? 54. Sarah invested $4000 at 5.2% interest compounded annually for 5 years. How much does Sarah have after 5 years?